SLOW COEVOLUTION OF A VIRAL PATHOGEN AND ITS DIPLOID HOST

We study a population exposed to a lethal infectious disease. Host res ponse is carried at one locus with two alleles while the pathogen occu rs in two variants. Based on an SI-type epidemic model we derive expli cit equations for the dynamics of each genotype. By assuming small var iations in both host and disease, we obtain a separation in time scale s between epidemic and evolutionary processes. This allows us to descr ibe explicitly the changes in host and disease gene frequencies. The r esulting model has a rich behaviour including multiple stable states a nd oscillations. However, in the oscillatory situation the model is de generate excluding the possibility of limit cycles. We show that the d egeneracy can only be removed by frequency dependent selection in the pathogen, for example by including direct interaction of virus in a fr ee-living stage. The qualitative conclusions extend to an SIR-type epi demic model, where recovery with immunity from the disease is possible .